Ghassan George Batrouni

Université Côte d'Azur

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Université Côte d'Azur

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Ghassan George Batrouni has a total of 157 co-authors. Here are the top co-authors by number of shared publications:

R. T. Scalettar
Physics Department, University of California, Davis, California 95616, USA
42 shared publications
Alex Hansen
Norwegian University of Science and Technology
21 shared publications
F. Hébert
Université Côte d'Azur, Centre National de la Recherche Scientifique, INPHYNI, Nice, France
20 shared publications
Valery G. Rousseau
Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
19 shared publications
Matthias Troyer
Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
12 shared publications
Jean Schmittbuhl
EOST/ITES Strasbourg University/CNRS Strasbourg France
9 shared publications

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- 19 October 2026
- Published by American Physical Society (APS) in Physical Review B
Emergence of charge density waves in the SU( N ) Holstein model at half filling
by Chunhan Feng, Linh Pham, George Batrouni, Richard T. Scalettar
From the condensed matter physics perspective, the most natural single orbital tight-binding Hamiltonians, and hence the most widely studied, contain two fermionic species, corresponding to spin-up and spin-down electrons. In cold atom systems, however, SU(N) symmetry, in which $N>2$ fermionic species reside within a single band, also occurs. To understand such experiments, the SU(N) Hubbard model has been increasingly studied. Here we present determinant quantum Monte Carlo simulations of the SU(N) Holstein Hamiltonian in which $N$ fermionic species couple to a single local phonon mode. We show that at half filling it has an insulating charge density wave phase (CDW) at low temperatures in which empty sites alternate with sites with $N$ particles. We determine the $N=3$ CDW phase diagram in the temperature $T$ versus electron-phonon coupling $\ensuremath{\alpha}$ plane at fixed phonon frequency ${\ensuremath{\omega}}_{0}$ and half filling $\ensuremath{\rho}=1.5$. The critical temperature ${T}_{c}$ for $N=3$ can be as high as two times the maximum attainable for $N=2$. We also obtain the $N$ dependence of ${T}_{c}$ for a representative, fixed, ${\ensuremath{\omega}}_{0}$ and $\ensuremath{\alpha}$.
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- 19 October 2026
- Published by American Physical Society (APS) in Physical Review B
Emergence of charge density waves in the SU( N ) Holstein model at half filling
by Chunhan Feng, Linh Pham, George Batrouni, Richard T. Scalettar
From the condensed matter physics perspective, the most natural single orbital tight-binding Hamiltonians, and hence the most widely studied, contain two fermionic species, corresponding to spin-up and spin-down electrons. In cold atom systems, however, SU(N) symmetry, in which $N>2$ fermionic species reside within a single band, also occurs. To understand such experiments, the SU(N) Hubbard model has been increasingly studied. Here we present determinant quantum Monte Carlo simulations of the SU(N) Holstein Hamiltonian in which $N$ fermionic species couple to a single local phonon mode. We show that at half filling it has an insulating charge density wave phase (CDW) at low temperatures in which empty sites alternate with sites with $N$ particles. We determine the $N=3$ CDW phase diagram in the temperature $T$ versus electron-phonon coupling $\ensuremath{\alpha}$ plane at fixed phonon frequency ${\ensuremath{\omega}}_{0}$ and half filling $\ensuremath{\rho}=1.5$. The critical temperature ${T}_{c}$ for $N=3$ can be as high as two times the maximum attainable for $N=2$. We also obtain the $N$ dependence of ${T}_{c}$ for a representative, fixed, ${\ensuremath{\omega}}_{0}$ and $\ensuremath{\alpha}$.
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Cited by 6
- 2 September 2025
- Published by American Physical Society (APS) in Physical Review B
Disorder and robustness of superconductivity on the quasi-one-dimensional flat-band Creutz lattice
by Si Min Chan, B. Grémaud, G. George Batrouni
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- 2 September 2025
- Published by American Physical Society (APS) in Physical Review B
Disorder and robustness of superconductivity on the quasi-one-dimensional flat-band Creutz lattice
by Si Min Chan, B. Grémaud, G. George Batrouni
Cited by 6
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- 15 November 2024
- Published by American Physical Society (APS) in Physical Review B
Field-induced Peierls order in systems of $S = 1$ Heisenberg spins coupled to quantum phonons
by Shifeng Cui, Wenan Guo, G. G. Batrouni, Pinaki Sengupta
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- 15 November 2024
- Published by American Physical Society (APS) in Physical Review B
Field-induced Peierls order in systems of $S = 1$ Heisenberg spins coupled to quantum phonons
by Shifeng Cui, Wenan Guo, G. G. Batrouni, Pinaki Sengupta
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Cited by 8
- 8 July 2024
- Published by American Physical Society (APS) in Physical Review B
Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model
by Maxwell Casebolt, Chunhan Feng, Richard T. Scalettar, Steven Johnston, G. G. Batrouni
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- 8 July 2024
- Published by American Physical Society (APS) in Physical Review B
Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model
by Maxwell Casebolt, Chunhan Feng, Richard T. Scalettar, Steven Johnston, G. G. Batrouni
Cited by 8
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Cited by 54
- 22 September 2022
- Published by American Physical Society (APS) in Physical Review B
Designer flat bands: Topology and enhancement of superconductivity
by Si Min Chan, B. Grémaud, G. G. Batrouni
We construct quasi-one-dimensional topological and nontopological three-band lattices with a tunable band gap and winding number of the flat band. Using full multiband mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we show explicitly how the band gap affects pairing and superconductivity (SC) in a Hubbard model with attractive interactions. We obtain excellent agreement between MF and DMRG calculations. The SC weight $D_{s}$ on the gapped topological, $W \neq 0$ , flat band increases linearly with interaction strength $U$ for low values and with a slope that depends on the details of the compact localized state at $U = 0$ . As $U \to 0$ for the gapped nontopological flat band ( $W = 0$ ), $D_{s}$ decays with a power law faster than quadratically but slower than exponentially. In the gapless case (flat band touching the band above it), we find at low $U$ (for both $W = 0$ and $W \neq 0$ ) that $D_{s} \propto U^{φ}$ , with $φ < 1$ . In other words, $D_{s}$ increases faster than linearly for low $U$ , thus favoring SC at weak interaction more than the gapped case. Our results reestablish that the BCS mean field and quantum metric alone are insufficient to characterize SC at weak coupling.
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- 22 September 2022
- Published by American Physical Society (APS) in Physical Review B
Designer flat bands: Topology and enhancement of superconductivity
by Si Min Chan, B. Grémaud, G. G. Batrouni
We construct quasi-one-dimensional topological and nontopological three-band lattices with a tunable band gap and winding number of the flat band. Using full multiband mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we show explicitly how the band gap affects pairing and superconductivity (SC) in a Hubbard model with attractive interactions. We obtain excellent agreement between MF and DMRG calculations. The SC weight $D_{s}$ on the gapped topological, $W \neq 0$ , flat band increases linearly with interaction strength $U$ for low values and with a slope that depends on the details of the compact localized state at $U = 0$ . As $U \to 0$ for the gapped nontopological flat band ( $W = 0$ ), $D_{s}$ decays with a power law faster than quadratically but slower than exponentially. In the gapless case (flat band touching the band above it), we find at low $U$ (for both $W = 0$ and $W \neq 0$ ) that $D_{s} \propto U^{φ}$ , with $φ < 1$ . In other words, $D_{s}$ increases faster than linearly for low $U$ , thus favoring SC at weak interaction more than the gapped case. Our results reestablish that the BCS mean field and quantum metric alone are insufficient to characterize SC at weak coupling.
Cited by 54
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Cited by 82
- 5 January 2022
- Published by American Physical Society (APS) in Physical Review B
Pairing and superconductivity in quasi-one-dimensional flat-band systems: Creutz and sawtooth lattices
by Si Min Chan, B. Grémaud, G. G. Batrouni
We study the pairing and superconducting properties of the attractive Hubbard model in two quasi-one-dimensional topological lattices—the Creutz and sawtooth lattices—which share two peculiar properties: each of their band structures exhibits a flat band with a nontrivial winding number. The difference, however, is that only the Creutz lattice is genuinely topological, due to a chiral (sublattice) symmetry, resulting in a quantized winding number and zero energy edge modes for open boundary conditions. We use a multiband mean field and exact density matrix renormalization group in our work. Our three main results are as follows: (a) For both lattice systems, the superconducting weight, $D_{s}$ , is linear in the coupling strength, $U$ , for low values of $U$ . (b) For small $U, D_{s}$ is proportional to the quantum metric for the Creutz system but not for the sawtooth system because its sublattices are not equivalent. We have therefore extended the approach to this more complex situation and found an excellent agreement with the numerical results. (c) At moderate and large $U$ , the conventional BCS mean field is no longer appropriate for such systems with inequivalent sublattices. We show that, for a wide range of densities and coupling strengths, these systems are very well described by a full multiband mean-field method where the pairing parameters and the local particle densities on the inequivalent sublattices are variational mean-field parameters.
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- 5 January 2022
- Published by American Physical Society (APS) in Physical Review B
Pairing and superconductivity in quasi-one-dimensional flat-band systems: Creutz and sawtooth lattices
by Si Min Chan, B. Grémaud, G. G. Batrouni
We study the pairing and superconducting properties of the attractive Hubbard model in two quasi-one-dimensional topological lattices—the Creutz and sawtooth lattices—which share two peculiar properties: each of their band structures exhibits a flat band with a nontrivial winding number. The difference, however, is that only the Creutz lattice is genuinely topological, due to a chiral (sublattice) symmetry, resulting in a quantized winding number and zero energy edge modes for open boundary conditions. We use a multiband mean field and exact density matrix renormalization group in our work. Our three main results are as follows: (a) For both lattice systems, the superconducting weight, $D_{s}$ , is linear in the coupling strength, $U$ , for low values of $U$ . (b) For small $U, D_{s}$ is proportional to the quantum metric for the Creutz system but not for the sawtooth system because its sublattices are not equivalent. We have therefore extended the approach to this more complex situation and found an excellent agreement with the numerical results. (c) At moderate and large $U$ , the conventional BCS mean field is no longer appropriate for such systems with inequivalent sublattices. We show that, for a wide range of densities and coupling strengths, these systems are very well described by a full multiband mean-field method where the pairing parameters and the local particle densities on the inequivalent sublattices are variational mean-field parameters.
Cited by 82
Open Access
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Cited by 20
- 25 September 2020
- Published by American Physical Society (APS) in Physical Review A
Nonlinear two-photon Rabi-Hubbard model: Superradiance, photon, and photon-pair Bose-Einstein condensates
by Shifeng Cui, B. Grémaud, Wenan Guo, G. G. Batrouni
We study the ground-state phase diagram of a nonlinear two-photon Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo simulations and density-matrix renormalization-group calculations. Our model includes a nonlinear photon-photon interaction term. Absent this term, the RH model has only one phase, the normal disordered phase, and suffers from spectral collapse at larger values of the photon-qubit interaction or intercavity photon hopping. The photon-photon interaction, no matter how small, stabilizes the system, which now exhibits two quantum phase transitions: Normal phase to photon-pair superfluid (PSF) transition and PSF to single-particle superfluid (SPSF). The discrete $Z_{4}$ symmetry of the Hamiltonian spontaneously breaks in two stages: First it breaks partially as the system enters the PSF and then it completely breaks when the system finally enters the SPSF phase. We show detailed numerical results supporting this, and map out the ground-state phase diagram.
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- 25 September 2020
- Published by American Physical Society (APS) in Physical Review A
Open Access
Nonlinear two-photon Rabi-Hubbard model: Superradiance, photon, and photon-pair Bose-Einstein condensates
by Shifeng Cui, B. Grémaud, Wenan Guo, G. G. Batrouni
We study the ground-state phase diagram of a nonlinear two-photon Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo simulations and density-matrix renormalization-group calculations. Our model includes a nonlinear photon-photon interaction term. Absent this term, the RH model has only one phase, the normal disordered phase, and suffers from spectral collapse at larger values of the photon-qubit interaction or intercavity photon hopping. The photon-photon interaction, no matter how small, stabilizes the system, which now exhibits two quantum phase transitions: Normal phase to photon-pair superfluid (PSF) transition and PSF to single-particle superfluid (SPSF). The discrete $Z_{4}$ symmetry of the Hamiltonian spontaneously breaks in two stages: First it breaks partially as the system enters the PSF and then it completely breaks when the system finally enters the SPSF phase. We show detailed numerical results supporting this, and map out the ground-state phase diagram.
Cited by 20
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Cited by 24
- 9 September 2019
- Published by American Physical Society (APS) in Physical Review A
Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: Photon-pair superradiance, Mott insulator, and normal phases
by Shifeng Cui, F. Hébert, B. Grémaud, V. G. Rousseau, Wenan Guo, G. G. Batrouni
We study the ground-state phase diagrams of two-photon Dicke, one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models using mean-field, perturbation, quantum Monte Carlo (QMC), and density-matrix renormalization-group methods. We first compare mean-field predictions for the phase diagram of the Dicke model with exact QMC results and find excellent agreement. The phase diagram of the JCH model is then shown to exhibit a single Mott insulator lobe with two excitons per site, a superfluid (SF, superradiant) phase and a large region of instability where the Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher Mott lobes. Also, unlike the one-photon case, the SF phases above and below the Mott lobe are surprisingly different: Below the Mott lobe, the SF consists of photon pairs as opposed to above the Mott lobe, where it is SF of simple photons. The mean-field phase diagram of the RH model predicts a transition from a normal to a superradiant phase but none is found with QMC.
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- 9 September 2019
- Published by American Physical Society (APS) in Physical Review A
Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: Photon-pair superradiance, Mott insulator, and normal phases
by Shifeng Cui, F. Hébert, B. Grémaud, V. G. Rousseau, Wenan Guo, G. G. Batrouni
We study the ground-state phase diagrams of two-photon Dicke, one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models using mean-field, perturbation, quantum Monte Carlo (QMC), and density-matrix renormalization-group methods. We first compare mean-field predictions for the phase diagram of the Dicke model with exact QMC results and find excellent agreement. The phase diagram of the JCH model is then shown to exhibit a single Mott insulator lobe with two excitons per site, a superfluid (SF, superradiant) phase and a large region of instability where the Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher Mott lobes. Also, unlike the one-photon case, the SF phases above and below the Mott lobe are surprisingly different: Below the Mott lobe, the SF consists of photon pairs as opposed to above the Mott lobe, where it is SF of simple photons. The mean-field phase diagram of the RH model predicts a transition from a normal to a superradiant phase but none is found with QMC.
Cited by 24
Open Access
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- 13 April 2019
- Published by arXiv in arXiv
Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: photon pair superradiance, Mott insulator and normal phases
by Shifeng Cui, F. Hébert, B. Grémaud, V. G. Rousseau, Wenan Guo, G. G. Batrouni
We study the ground state phase diagrams of two-photon Dicke, the one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models using mean field, perturbation, quantum Monte Carlo (QMC), and density matrix renormalization group (DMRG) methods. We first compare mean field predictions for the phase diagram of the Dicke model with exact QMC results and find excellent agreement. The phase diagram of the JCH model is then shown to exhibit a single Mott insulator lobe with two excitons per site, a superfluid (SF, superradiant) phase and a large region of instability where the Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher Mott lobes. Also unlike the one-photon case, the SF phases above and below the Mott are surprisingly different: Below the Mott, the SF is that of photon {\it pairs} as opposed to above the Mott where it is SF of simple photons. The mean field phase diagram of the RH model predicts a transition from a normal to a superradiant phase but none is found with QMC.
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- 13 April 2019
- Published by arXiv in arXiv
Open Access
Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: photon pair superradiance, Mott insulator and normal phases
by Shifeng Cui, F. Hébert, B. Grémaud, V. G. Rousseau, Wenan Guo, G. G. Batrouni
We study the ground state phase diagrams of two-photon Dicke, the one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models using mean field, perturbation, quantum Monte Carlo (QMC), and density matrix renormalization group (DMRG) methods. We first compare mean field predictions for the phase diagram of the Dicke model with exact QMC results and find excellent agreement. The phase diagram of the JCH model is then shown to exhibit a single Mott insulator lobe with two excitons per site, a superfluid (SF, superradiant) phase and a large region of instability where the Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher Mott lobes. Also unlike the one-photon case, the SF phases above and below the Mott are surprisingly different: Below the Mott, the SF is that of photon {\it pairs} as opposed to above the Mott where it is SF of simple photons. The mean field phase diagram of the RH model predicts a transition from a normal to a superradiant phase but none is found with QMC.
Open Access
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Cited by 19
- 6 October 2015
- Published by American Physical Society (APS) in Physical Review A
Berry curvature of interacting bosons in a honeycomb lattice
by Yun Li, Pinaki Sengupta, George G. Batrouni, Christian Miniatura, Benoît Grémaud
We consider soft-core bosons with on-site interaction loaded in the honeycomb lattice with different site energies for the two sublattices. Using both a mean-field approach and quantum Monte Carlo simulations, we show that the topology of the honeycomb lattice results in a nonvanishing Berry curvature for the band structure of the single-particle excitations of the system. This Berry curvature induces an anomalous Hall effect when driving the system out of equilibrium. It is seen by studying the time evolution of a wave packet, namely, a superfluid ground state in a harmonic trap, subjected either to a constant force (Bloch oscillations) or to a sudden shift of the trap center.
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- 6 October 2015
- Published by American Physical Society (APS) in Physical Review A
Open Access
Berry curvature of interacting bosons in a honeycomb lattice
by Yun Li, Pinaki Sengupta, George G. Batrouni, Christian Miniatura, Benoît Grémaud
We consider soft-core bosons with on-site interaction loaded in the honeycomb lattice with different site energies for the two sublattices. Using both a mean-field approach and quantum Monte Carlo simulations, we show that the topology of the honeycomb lattice results in a nonvanishing Berry curvature for the band structure of the single-particle excitations of the system. This Berry curvature induces an anomalous Hall effect when driving the system out of equilibrium. It is seen by studying the time evolution of a wave packet, namely, a superfluid ground state in a harmonic trap, subjected either to a constant force (Bloch oscillations) or to a sudden shift of the trap center.
Cited by 19

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